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Harmonic morphisms and conformal foliations by geodesics of three-dimensional space forms

Part of: Variational problems in infinite-dimensional spaces Higher-dimensional theory Global differential geometry

Published online by Cambridge University Press:  09 April 2009

Paul Baird  and
John C. Wood
John C. Wood
Affiliation:
Department of Pure Mathematics University of LeedsLeeds LS29JT United Kingdom
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Abstract

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A complete classification is given of harmonic morphisms to a surface and conformal foliations by geodesics, with or without isolated singularities, of a simply-connected space form. The method is to associate to any such a holomorphic map from a Riemann surface into the space of geodesics of the space form. Properties such as nonintersecting fibres (or leaves) are translated into conditions on the holomorphic mapping which show it must have a simple form corresponding to a standard example.

MSC classification

Secondary: 53C12: Foliations (differential geometric aspects) 58E20: Harmonic maps , etc. 31B99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 51 , Issue 1 , August 1991 , pp. 118 - 153
Copyright
Copyright © Australian Mathematical Society 1991

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